共线散射体系A+BC的平-振能量传递──无限维李代数处理方法

利用无限维李代数方法处理了在BC分子能谱中含有二级与三级非简谐项的散射体系A＋BC的平-振能量传递问题，获得了散射过程的含有主要动力学参量的跃迁矩阵元和跃迁几率的解析表达式     

量子反应散射的动力学李代数方法

用动力学李代数方法描述了量子反应散射问题 .对共线交换反应A BC→AB C ,得到了含有主要动力学参数的反应跃迁几率的解析表达式 .计算了共线反应散射过程H H2 (n =0 )→H2 (n′ =0 ) H的反应跃迁几率 .结果表明 ,动力学李代数方法对计算反应几率是非常有效的 .     

构造SO~2分子势能面的李代数方法

把李代数方法得到的SO~2分子的代数Hamiltonian,利用相干态基经典化并找到一个新的变换,将分子的键角引入,而得到SO~2分子的势能面。由该势能面计算的解离能,所给出的势能面的立体图和相应的等高线以及力常数与其他方法给出的相一致。该方法可以推广到多原子分子及反应体系。     

准线型四原子分子高激发振动能级的动力学李代数方法

近几年来 ,人们用李代数方法处理了许多问题 [1～ 5] ,在此基础上 ,我们利用动力学李代数方法研究了准线型四原子分子高激发振动态 ,把分子的 Hamiltonian展开成 Casimir算子与 Majorana算子之和[6,7] ,然后进行代数处理 ,从而得到了代数 Hamiltonian的本征值 .1　基本理论四原子分子有 3个键 ,所满足的对称群为 G=U1(4) U2 (4) U3 (4) ,处理分子问题时 ,一般要考Fig.1　 The bond coordinates of fulminic acid(HCNO)虑键与键之间的耦合 ,为了方便 ,首先让键 1与键 2耦合 ,然后再与键 3耦合 (图 1 ) .这种耦合方式可记为 (1 2 ) 3 …     

A+BC共线碰撞能量传递的动力学李代数结合中间绘景研究

在半经典近似下将动力学李代数方法和中间绘景结合应用于原子-双原子分子(非谐振子)共线碰撞中的平动-振动传能的研究。在群参量的一级近似下求解群参量的运动方程,进而确定时间演化算符。并以散射体系H₂+He为例,计算了H₂分子的振动跃迁几率,计算结果与精确量子力学计算结果符合得较好。     

取代苯体系的二阶非线性光学性质:动力学李代数方法

提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用.     

非线性三原子分子高激发振动态的理论研究: Lie代数方法

利用Ｌｉｅ代数方法研究了弯曲三原子分子的振动高激发态能谱，并以ＳＯ_２为例， 拟合 ３０条光谱能级得到的 ＲＭＳ误差是 １．６６ ｃｍ~－１．结果表明，所得到的分子 Ｈａｍｉｌｔｏｎｉａｎ 的代数展开式可以很好地再现实验能级，它预测了ＳＯ_２分子振动总量子数达１０的全部 振动能级．从得到的该代数Ｈａｍｉｌｔｏｎｉａｎ还可以得到势能面等．     

Lie代数方法在线形三原子分子转动谱计算中的应用

利用动力学群U₁(4)ÄU₂(4)的对称性质以及相应的Lie代数给出了描写线形三原子分子振转谱的Hamilton量. 在考虑了振转相互作用后, 所得上述Hamilton量本征值的表达式具有在光谱分析计算中常用的项值方程的形式. 利用此表达式拟合观察线位可以得到分子的振转常数. 作为算例, 对N₂O及HCN分子(02⁰0-01¹0)ν₂红外跃迁谱带的转动能级进行了拟合分析, 所得均方根误差分别为0.00001和0.0014 cm^-1.     

N-(1-萘基)-琥珀酰亚胺化合物晶体结构的理论预测

用Materials Studio软件对N-(1-萘基)-琥珀酰亚胺多晶粉末的X射线衍射数据进行衍射峰指标化、晶胞参数优化和空间群搜索等理论计算, 可以确定晶体结构所属的晶系和空间群, 并初步给出和多晶粉末衍射数据相近的晶胞参数; 在已确定空间群范围内, 以密度泛函理论计算得到的最低能量构象作为初始分子结构, 对N-(1-萘基)-琥珀酰亚胺多晶进行晶体结构理论预测, 给出一系列假定的晶胞参数, 从中可以找到和经上述计算给出的晶胞参数一致的晶体结构；对其进行晶胞参数优化后, 得到晶体结构具有和多晶粉末X射线衍射数据相近的衍射曲线, 并与已有的单晶数据相吻合.     

Lie algebraic approach to multiphoton excitation of diatomic molecules in intense laser fields

The quadratic anharmonic oscillator Lie algebraic model is used to study the multiphoton transition of the diatomic molecule placed in intense laser fields. The multiphoton excitation of vibration and vibration‐rotation of diatomic molecules in intense laser fields are discussed. In the pure vibration transition we calculate the transition probability versus the frequency of the laser fields for the CO molecule. We also investigate the roles of rotational motion in multiphoton processes and compare with pure vibration for the LiH molecule. The influences of the angular quantum number l and the molecular orientations in laser fields on the multiphoton processes are discussed. The averaged absorb energy changing with the laser field's frequency is calculated. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 201–207, 1999     

H_2O振动高激发态的李代数研究

Ｈ_２Ｏ振动高激发态的李代数研究郑雨军，丁世良（山东大学理论化学研究室，济南２５０１００）（山东师范大学物理系，济南２５００１４）１引言多原子分子的振动高激发态是当前理论研究和实验研究的重要课题之一．近来对振动高激发态光谱数据的精确测量，更引起了人们?..     

Theoretical study of highly vibrational states of nonlinear triatomic molecules using Lie algebraic approach

The vibrational excitations of bent triatomic molecules are studied by using Lie algebra. The RMS error of fitting 30 spectroscopic data is 1.66 cm-1 for SO2. The results show that the expansion of a molecular algebraic Hamiltonian can well describe the experimental data. And the total vibrational levels can be calculated using this Hamiltonian. At the same time, the potential energy surface can also be obtained with the algebraic Hamiltonian.     

A dynamical Lie algebraic mehtod for quantum reactive scattering

Ｒａｐｉｄｐｒｏｇｒｅｓｓｉｎｔｈｅｔｈｅｏｒｙｏｆｑｕａｎｔｕｍｒｅａｃｔｉｖｅｓｃａｔｔｅｒｉｎｇｈａｓｂｅｅｎｍａｄｅｉｎｔｈｅｐａｓｔｆｅｗｙｅａｒｓ.Ａｓａｒｅｓｕｌｔｏｆｔｈｅｐｒｏｇｒｅｓｓｏｎｅｃａｎｎｏｗｃａｌｃｕｌａｔｅｅｘａｃｔｓｔａｔｅ＿ｔｏｓｔａｔｅｒｅａｃｔｉｏｎｃｒｏｓｓｓｅｃｔｉｏｎｓｆｏｒａｆｅｗｆｕｎｄａｍｅｎｔａｌｒｅａｃｔｉｏｎｓ.Ａｍｏｎｇｖａｒｉｏｕｓｆｏｒｍｕｌａｔｉｏｎｓｏｆｔｈｅｔｈｅｏｒｅｔｉｃａｌａｐｐｒｏａｃｈ,ｔｈｅＳｍａｔｒｉｘＫｏｈｎｖ…     

Theoretical study of nonlinear triatomic molecular potential energy surfaces: Lie algebraic method

Triatomic molecular potential energy surfaces (PES) are obtained by using coherent state to take the classical limits of algebraic Hamiltonian. The algebraic Hamiltonian for bent tria-tomic molecules can be obtained using Lie algebraic method (the expansion coefficients are obtained by fitting spectroscopic data). This PES is applied to H2O molecule, and good results are obtained.     

Application of the Lie algebraic approach to diffractionally and rotationally inelastic molecule–surface scattering

The Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 , 89 (1978)] is applied to the molecule–surface scattering. Specially, the diffractionally and rotationally inelastic scattering of a diatomic molecule from a solid surface is dealt with. Within the framework of the close-coupling method, we construct a Hamiltonian for the scattering system and use it to generate a dynamical algebra h₆. By solving equations of motion for the group parameters, the scattering wave functions near the surface are obtained. Computed transition probabilities of diffractively and rotationally inelastic scattering of H₂ from LiF(001) surface with the use of Lie algebraic method are seen to agree well with the coupled-channel calculations. The Lie algebraic method thus appears to have a wide range of validity for describing the dynamics of gas–surface scattering. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 981–989, 1997     

Quantum dynamics of dissociative adsorption of H2 on Ni(100) using the dynamical Lie algebraic method

A dynamical Lie algebraic method has been applied to treating the quantum dynamics of dissociative adsorption of H₂ on a static flat metal surface. An LEPS potential energy surface has been used to describe the interaction of H₂ with Ni(100) surface. The dependence of the initial state-selected dissociation probability was obtained analytically on the initial kinetic energy and time. A comparison with other theoretical calculations and experiments is made. The results show that the method can be effectively used to describe the dynamics of reactive gas-sdace scattering. Project supported by the National Natural Science Foundation of China (Grant No. 19694033) and partially by the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University (Grant No. 9801).